Compactifications of moduli spaces of K3 surfaces with a nonsymplectic involution

2022/08/22 by Valery Alexeev, Alexeev, Valery, Philip Engel +1 · 1 citation
Mathematics · #14D22 #14J28 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2208.10383

openalex publication_date 2022/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

There are 75 moduli spaces F_S of K3 surfaces with a nonsymplectic involution. We give detailed descriptions of Kulikov models for one-parameter degenerations in F_S. In the 50 cases where the fixed locus of the involution has a component C_g of genus g≥2, we identify normalizations of the KSBA compactifications of F_S via stable pairs (X,εC_g), with explicit semitoroidal compactifications of F_S.

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• Polync varieties and multiparameter Kulikov models

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